Blade machining system error compensation method based on error decomposition and kalman filtering

Abstract

This invention discloses a method for compensating system errors in blade machining based on error decomposition and Kalman filtering, comprising: Step 1: calculating the profile error of each cross section; Step 2: obtaining the system profile error after removing random errors; Step 3: converting the system profile error into three-dimensional coordinates and fitting them into closed curves, grouping them according to cross section height; Step 4: obtaining the final profile error compensation value of the thin-walled blade at the discrete point position; Step 5: obtaining the coordinates of the profile error compensation point, performing torsion and offset compensation on the coordinates of the profile error compensation point to obtain the final compensation point cloud coordinates, and then obtaining the compensation curve of each cross section; This invention can effectively improve the machining accuracy of thin-walled blades by decomposing the measurement error into systematic errors and random errors, and using Kalman filtering to perform optimal estimation of the systematic errors, significantly reducing the interference of random noise, thereby achieving control over the consistency of machining accuracy of batch blades.

Description

Technical Field

[0001] This invention belongs to the field of blade machining, and particularly relates to an error compensation method for blade machining systems based on error decomposition and Kalman filtering. Background Technology

[0002] Integral bladed disks (IBDs) are key components for achieving structural innovation and technological breakthroughs in next-generation aero-engines. They bear the important mission of improving engine performance. IBD structures are widely used in the design and manufacturing of next-generation high-performance aero-engines. IBD structures eliminate tenon-like airflow losses, reducing the overall weight and number of parts. Aerodynamically, they employ wide-chord, swept blades and narrow flow channels, significantly improving aerodynamic efficiency. The machining precision of IBD blades has a crucial impact on engine aerodynamic performance. Precise blade profiles and smooth surfaces ensure smoother airflow over the blade surface, reducing airflow separation and vortices, thereby improving engine intake efficiency and thrust.

[0003] Aero-engine integral bladed disks (IBDs) are typical cantilever beam structures with complex geometry, characterized by a twisted blade body, complex leading and trailing edges, and variable cross-section airfoils, all within a narrow flow channel. To meet the design requirements of weight reduction and efficiency improvement in aero-engines, blade structures are becoming increasingly complex and their wall thickness is continuously decreasing, especially in the leading, trailing, and tip regions of open IBD blades, where the thickness is even less than 0.1 mm. Blades often use difficult-to-machine materials such as titanium alloys and high-temperature alloys, exhibiting high thermal hardness and strength. Due to these structural and material properties, blades are highly susceptible to elastic deformation and residual stress deformation during machining, leading to difficulties in achieving design accuracy and severely impacting the compressor's aerodynamic performance. Because of the integral structure, any deviation in the dimensional or positional tolerances of any single blade can result in the entire IBD being defective or even scrapped. Therefore, error compensation methods are needed to control the machining accuracy of thin-walled blades.

[0004] After the thin-walled blades are machined, the machining errors obtained through measurement can be divided into: systematic errors, which exhibit a certain degree of stability and repeatability due to the influence of machining parameters, workpiece stiffness, etc., and random errors influenced by environmental factors. If a compensation model is directly established based on the measured data, it is easily affected by random errors, resulting in undercompensation or overcompensation.

[0005] Currently, research on error compensation methods for thin-walled blade machining largely focuses on directly constructing error compensation models based on measurement data. This approach is prone to random errors, leading to inaccurate models. Therefore, when modeling errors based on measured data, the raw data needs to be processed to remove the interference of random errors. Furthermore, existing compensation methods do not consider changes in the machining system over time, such as the aging of machine tools and fixtures causing variations in machining accuracy. This results in compensation models built based on historical machining error data being unable to meet the needs of the current process system. Summary of the Invention

[0006] The purpose of this invention is to provide an error compensation method for blade processing systems based on error decomposition and Kalman filtering, in order to solve the problems that existing thin-walled blade error compensation modeling is easily affected by random errors, and does not take into account the time-series aging changes of the process system, resulting in poor model adaptability.

[0007] This invention adopts the following technical solution: an error compensation method for blade machining systems based on error decomposition and Kalman filtering, comprising: Step 1: Obtain the measuring points of each section of the processed blade, and project each measuring point onto the corresponding measuring section. Calculate the profile error of each section based on the theoretical section line and the corresponding projection point. Step 2: Sort the profile error of each blade detection section and construct the profile error signal. Use a hybrid algorithm of wavelet threshold denoising combined with amplitude protection SG filtering to process the signal and separate the system profile error after removing random errors. Step 3: Convert the system profile error into three-dimensional coordinates and fit it into a closed curve, grouping them according to the cross-sectional height; obtain discrete points on the theoretical cross-sectional line using the isochord height sampling method with distance constraints; find the intersection point of the line segment from the discrete points, and use the distance between the theoretical point and the intersection point as the compensation value for the blade cross-sectional profile error; Step 4: For the profile error compensation value at the same discrete point, input the error observation value at that position in sequence according to the time order of blade processing, and perform recursive optimal estimation on the sequence data based on the Kalman filter algorithm to obtain the final profile error compensation value of the thin-walled blade at that discrete point. Step 5: Offset each discrete point along the opposite direction of the actual deformation of the blade profile to obtain the corresponding final profile error compensation value to obtain the profile error compensation point coordinates. Perform torsion and offset compensation on the profile error compensation point coordinates to obtain the final compensation point cloud coordinates, and then obtain the compensation curve of each section.

[0008] The beneficial effects of this invention are: This invention can effectively improve the machining accuracy of thin-walled blades. By decomposing the measurement error into systematic error and random error, and using Kalman filtering to make the optimal estimate of the systematic error, the interference of random noise is significantly reduced, thereby achieving precise control of the machining consistency of batch blades. This invention introduces a signal extension method to effectively suppress boundary effects in the wavelet decomposition process. By reasonably extending both ends of the signal, new spikes or abrupt changes are avoided at the junction of the first and last ends of the filtered signal, ensuring a smooth transition of the filtered signal at the junction point. This ensures the geometric continuity and smoothness of the reconstructed cross-sectional curve, providing high-quality contour data for subsequent error compensation. This invention can adaptively identify rough regions in contour error signals; based on this, it adopts an amplitude protection strategy to selectively retain the original error values ​​of peak regions, preventing key features such as the leading and trailing edges of the blade from being over-smoothed, thereby effectively suppressing random noise while maximizing the preservation of the geometric features of the blade, achieving the best balance between noise suppression and feature preservation. This invention employs Kalman filtering for recursive estimation of system errors, ensuring that the calculated system error values ​​reflect the actual state of the current process system in real time, including factors that change slowly over time, such as machine tool spindle wear and fixture positioning offset. When new machining data (such as the measured error of subsequent batches of blades) is input, the Kalman filter can update the system error estimate online, making the compensation adaptive and continuously meeting the dynamic needs of the machining system, significantly improving the robustness and engineering practicality of the compensation method. Attached Figure Description

[0009] Figure 1 This is a diagram showing the WT-AP-SG denoising effect without signal extension in step 2 of the present invention; Figure 2 This is a diagram showing the WT-AP-SG denoising effect achieved by signal extension in step 2 of this invention. Figure 3 This is a diagram showing the Savitzky-Golay filter effect without amplitude protection in step 2 of this invention. Figure 4 This is a diagram showing the effect of the Savitzky-Golay filter using amplitude protection in step 2 of the present invention. Detailed Implementation

[0010] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0011] This invention discloses an error compensation method for blade processing systems based on error decomposition and Kalman filtering, comprising five steps.

[0012] Step 1: Obtain the measuring points of each section of the processed blade, and project each measuring point onto the corresponding measuring section. Calculate the profile error of each section based on the theoretical section line and the corresponding projection point.

[0013] First, a coordinate measuring machine is used to perform equal-section scanning measurements on the machined thin-walled blade to obtain discrete measurement points on each section. Each measurement point is then projected onto the corresponding measurement section to eliminate minor fluctuations in the Z-axis direction and ensure the planar consistency of the measurement data.

[0014] Subsequently, the projected measured points and theoretical cross-sectional lines are spatially registered, and the optimal matching between the two is achieved through coordinate transformation, thereby obtaining the profile error, position error and torsion angle error of each cross-section.

[0015] Step 2: Sort the profile error of each blade detection section and construct the profile error signal. Use a hybrid algorithm of wavelet threshold denoising combined with amplitude protection SG filtering to process the signal and separate the system profile error after removing random errors.

[0016] Step 2 specifically involves: for each detection section of the blade, sequentially numbering the contour error along the contour detection path of each section; converting the ordered contour error data into contour error signals for each section; and using a hybrid filtering algorithm combining wavelet threshold denoising and Savitzky-Golay filtering with amplitude protection to decompose the contour error signals of each section to obtain the system contour error after removing random errors on each section.

[0017] The contour errors on each cross section are sequentially numbered according to the detection path and converted into a one-dimensional signal form. That is, in the Cartesian coordinate system, the sequence number of the detection point is used as the abscissa and the contour error value corresponding to each point is used as the ordinate to construct a signal sequence that reflects the distribution change of the error along the cross section contour.

[0018] Because the original signal can be smoothly joined end-to-end to form a closed signal, boundary effects can cause new spikes at the connection points of the filtered signal during wavelet filtering and other processing, making the connection points uneven. Figure 1 As shown. To address this issue, a signal extension method is employed to suppress boundary effects. Specifically, 40 data points are extended outwards from both the beginning and end of the signal: the data segment at the tail of the one-dimensional signal with contour error is copied and spliced ​​to the beginning of the signal, while the data segment at the beginning of the signal is copied and spliced ​​to the tail. Through this extension, the boundary effects generated during the hybrid filtering process are effectively shifted to the extended regions at both ends, thereby ensuring the smoothness of the connection between the beginning and end, as shown. Figure 2 As shown.

[0019] The specific steps of processing the signal using the hybrid algorithm of wavelet threshold denoising combined with amplitude-protected SG filtering in step 2 are as follows: First, the wavelet threshold denoising algorithm is used to perform preliminary denoising on the contour error signals of each cross section to remove most of the high-frequency noise; second, the rough region detection is performed on the wavelet denoising results to divide the rough regions that require special processing; then, SG filtering with amplitude protection is applied to the rough regions, and standard SG filtering is applied to the smooth regions; finally, the processing results of the two types of regions are fused and lightly smoothed.

[0020] While wavelet thresholding can separate high-frequency noise from low-frequency effective components through multi-scale decomposition, its ability to suppress uniformly distributed spikes is limited, and hard thresholding easily introduces signal oscillations. Savitzky-Golay (SG) filtering excels at smoothing random noise and preserving signal trends, but its fixed polynomial fitting window performs poorly with non-uniformly distributed noise and abrupt spikes. Although using SG filtering after wavelet thresholding can compensate for some of the shortcomings of wavelets, the excessive smoothing in local areas caused by SG filtering introduces new problems, such as… Figure 3 As shown. Amplitude protection can effectively preserve useful information by targeting peak fluctuation regions. Amplitude protection selectively preserves the original values ​​of peak regions, preventing core features from being overly smoothed, thus achieving a balance between noise suppression and feature preservation. Figure 4 As shown.

[0021] Before implementing amplitude protection, it is necessary to identify regions of severe fluctuation or spikes in the signal. Therefore, the input signal is first analyzed to obtain its dynamic range and standard deviation as baseline parameters for subsequent processing. The dynamic range R and standard deviation σ of the signal are calculated, assuming the input signal is... N is the signal length, as shown in equations (1) and (2).

[0022] (1) (2) To accurately identify significant fluctuation regions (referred to as "rough regions") in a signal that require special processing, the algorithm constructs a "roughness index" through multi-feature fusion. A sliding window is used to calculate the local statistical characteristics of the signal, including the local standard deviation σ, which reflects the degree of signal dispersion within the window. i The gradient magnitude g, which reflects the local rate of change of the signal. i The curvature c, which reflects the second rate of change of the signal. i Peak detection for identifying sudden spikes in signals. i See equations (3)-(6).

[0023] Local standard deviation: (3) Gradient magnitude: (4) Curvature: (5) Peak detection: (6) Where M is the window size, This represents the moving average value centered at i with a width of d. After normalizing and weighting the features, the roughness index r is used for fusion. i The calculation formula is: (7) The mean and standard deviation of the roughness index are μ. r and σ r : (8) (9) In order to adaptively distinguish between rough and smooth regions, this invention defines a dynamic threshold. The calculation of the threshold is based on empirical rules in statistics. Regions with a roughness index greater than the threshold are classified as rough regions. The threshold is calculated as shown in equation (10).

[0024] (10) The value of coefficient α is adjusted according to the signal characteristics: when R>0.05, α is 0.8 to capture more details of signals with a large dynamic range; when R≤0.05, α is 1.5 to avoid misjudging noise as a coarse region. The switching threshold of 0.05 is an empirical threshold determined based on the signal energy distribution characteristics.

[0025] Amplitude protection constrains amplitude changes at specific points during the filtering process based on the local dynamic characteristics of the signal. The local amplitude A of the signal is defined. i This parameter reflects the degree of dynamic change of the signal within a local range, as shown in equation (11). (11) Among them, s i,L Let i represent a local signal segment with length L centered at point i, where L is the length of the local analysis window. The global average amplitude is calculated as shown in equation (12), which serves as a benchmark for subsequent amplitude change evaluation.

[0026] (12) Amplitude protection is applied to the detected rough areas, and the filter amplitude change is set to be less than [a certain value]. Only when the filtering result is received will the filter result be accepted, as shown in equation (13).

[0027] (13) Among them, s i,f s represents the filtered value at the i-th data point. i,o This represents the original value at the i-th data point. This represents the absolute value of the change in value before and after filtering. Based on the 3dB principle in signal processing, γ is set to 0.3 for peak regions to prioritize the preservation of abrupt changes. For non-peak regions in coarse areas, a more lenient constraint is adopted, with γ empirically set to 0.45, aiming to preserve features while also achieving good noise reduction.

[0028] Step 3: Convert the system profile error into three-dimensional coordinates and fit it into a closed curve, grouping them according to the cross-sectional height; obtain discrete points on the theoretical cross-sectional line using the isochord height sampling method with distance constraints; find the intersection point of the line segment from the discrete points, and use the distance between the theoretical point and the intersection point as the compensation value for the blade cross-sectional profile error.

[0029] Step 3 specifically involves: The system contour error is converted into three-dimensional point coordinates and fitted into a closed curve. The closed curves are grouped according to the cross-sectional height, so that the closed curves in the same group correspond to the same theoretical cross-sectional line; The equal chord height sampling method with distance constraints is used to discretize each theoretical cross-section line to generate multiple discrete points with equal chord height constraints; By constructing normal line segments at each discrete point, and intersecting them with the closed curves of each blade in the group, the intersection point is obtained. The Euclidean distance between the intersection point and the corresponding discrete point is the profile error compensation value of a single blade at that cross-sectional position.

[0030] Therefore, firstly, the contour error of each blade after removing random errors on each cross section is converted into three-dimensional point coordinates, and the conversion relationship is shown in Equation (14). On this basis, non-uniform rational B-splines (NURBS) are used to fit the point cloud of each cross section into a closed curve to establish a continuous geometric contour model, which facilitates subsequent error analysis and discrete sampling.

[0031] (14) In the formula, (x c,i , y c,i , z c,i The point cloud coordinates (x) are obtained after registering the projection points of the original measurement points of each cross-section with the theoretical cross-section line. r,i , y r,i , z r,i ) represents the intersection of the theoretical cross-section line and the point (x). c,i , yc,i , z c,i The coordinates of the points with the shortest distance, d t,i The contour error of the point; n i After removing random errors, the profile error of the points is removed, (x a,i , y a,i , z a,i () represents the coordinates of a 3D point after random error removal.

[0032] Subsequently, the fitted closed curves are grouped according to the cross-sectional height to ensure that the closed curves in the same group correspond to the same theoretical cross-sectional line. The theoretical profile of each cross-section is discretized using the equal chord height sampling method, generating a series of discrete points with equal chord height constraints. A normal line segment is drawn through each discrete point, intersecting with the closed curve of each blade in the group to obtain the intersection point; the Euclidean distance between the intersection point and the corresponding theoretical discrete point is the blade cross-sectional profile error compensation value at that cross-sectional position.

[0033] In step 3, the isochordal height sampling method with distance constraints introduces the maximum distance control parameter L. max This refers to the maximum allowable distance between two discrete points; the specific steps are as follows: Step a: Set P0 as the starting point and set it as the current point P. p ; Step b: Perform an iterative search using the equal chord height method to determine the next potential measurement point P. n Make the current point P p With P n The chord height is h; Step c: Calculate P p With prediction point P n The distance d between them; if d > L max Then we reject the prediction of point P. n Instead, follow the curved path with a fixed step size L. max Determine the next measurement point P new If d≤L max Then accept the prediction point P. n For the next measurement point P new ; Step d: Update the current point to P new Repeat steps b through c until the process ends; Step e: Export the obtained data points, which are the discrete points.

[0034] Step 4: For the profile error compensation value at the same discrete point, input the error observation value at that position sequentially according to the time sequence of blade processing, and perform recursive optimal estimation on the sequence data based on the Kalman filter algorithm to obtain the final profile error compensation value of the thin-walled blade at that discrete point.

[0035] Step 4 specifically involves: sequentially deriving the error values ​​at each discrete point according to the blade numbering order to form an error sequence facing the same cross-section and the same location. Based on this, for the profile error at the same discrete point, the error observation values ​​at that location are sequentially input according to the blade processing time sequence. The Kalman filter algorithm is used to recursively estimate the optimal value of the sequence data, thereby obtaining the final profile error compensation value of the thin-walled blade at that discrete point.

[0036] Kalman filtering is a linear optimal estimation algorithm based on a state-space model. Its core advantage lies in its ability to recursively update the optimal estimate of the current state using the state estimate from the previous moment and the observation from the current moment. This algorithm not only offers real-time performance but also updates the estimated system error in real time when new processing data (such as measurement results from subsequent batches of blades) is input, allowing the compensation model to adaptively track the time-varying characteristics of the process system. Therefore, using Kalman filtering for system error estimation ensures that the calculated system error value accurately reflects the actual state of the current process system, effectively compensating for systematic deviations caused by factors such as machine tool spindle wear and fixture positioning offsets.

[0037] Step 5: Offset each discrete point along the opposite direction of the actual deformation of the blade profile to obtain the corresponding final profile error compensation value to obtain the profile error compensation point coordinates. Perform torsion and offset compensation on the profile error compensation point coordinates to obtain the final compensation point cloud coordinates, and then obtain the compensation curve of each section.

[0038] The method for torsional and offset compensation in step 5 is as follows: The positional error and torsional angle error of each section are calculated based on the theoretical section line and the corresponding projection point. The system positional error and system torsional angle error are obtained based on Kalman filtering. Then, the coordinates of each profile error compensation point are twisted and offset in the opposite direction of the actual deformation of the blade profile along the normal vector to obtain the corresponding system positional error and system torsional angle error, thus obtaining the final compensation point cloud coordinates.

[0039] Using the same method, Kalman filtering was applied to the positional and torsional angle errors of each section in the X and Y directions to obtain the corresponding system positional and torsional angle errors. These estimation results provide optimal estimates of the system errors for the subsequent construction of the error compensation model, laying a data foundation for the high-precision machining of thin-walled blades.

[0040] The corresponding final profile error compensation value n is shifted from each discrete point in the opposite direction of the actual deformation of the blade profile along the normal vector. j *The coordinates of the contour error compensation point are obtained, as shown in Equation (15). This process is based on the principle of inverse deformation. By applying a geometric correction equal in magnitude and opposite in direction to the system contour error in advance on the theoretical surface, the system contour error generated during the processing is offset.

[0041] (15) In the formula, (x q,j , y q,j , z q,j (x) represents the coordinates of a discrete point on the theoretical contour line. n,j , y n,j , z n,j ) represents the unit normal vector passing through discrete points on the theoretical contour line, and n j * represents the final contour error compensation value, (x) s,j , y s,j , z s,j ) represents the coordinates of the point after contour error compensation.

[0042] Secondly, the point set obtained after compensation for each cross-section is treated as a whole and subjected to rotational transformation. Through the above rotational operation, the overall torsional deviation generated during the blade manufacturing process can be effectively compensated.

[0043] Subsequently, the rotated point set is subjected to a translation transformation. This translation transformation aims to eliminate the systematic positional errors of the blade at each cross-section.

[0044] Finally, non-uniform rational B-splines (NURBS) were used to fit curves to the point sets of each translated section, generating a compensation curve for each section. Based on this, a lofting operation was used to construct a continuous NURBS surface from the curves of each section, thus obtaining the compensated geometric model. This model integrates comprehensive compensation information from multiple sources of systematic errors, such as profile accuracy, position accuracy, and torsion angle, and can fully reflect the reverse correction effect of machining systematic errors, providing a reliable geometric benchmark for the subsequent high-precision machining of thin-walled blades.

[0045] Example Taking the TC17 aero-engine titanium alloy integral bladed disk blade as an example, the effectiveness of the proposed compensation method was verified. A cuboid block was used as the blank, with dimensions of 260mm x 145mm x 54mm. A total of 8 blank blocks were machined, and each blank block could be machined into 5 blades, resulting in a total of 40 experimental blade samples. To ensure the traceability of the experimental process, each blank block and its corresponding blade were independently numbered and marked, and its machining sequence and process parameters were fully recorded. The Kede KMC800SU five-axis vertical machining center was used as the experimental platform. Carbide tapered ball end mills were used for blade milling due to their wear resistance and high hardness. Based on experience, the process parameters and tool selection for each machining process were determined. The cutting parameters and tool parameters for roughing, semi-finishing, and finishing are listed in Tables 1 and 2.

[0046] Table 1 Roughing parameters Table 2 Semi-finishing and finishing parameters After completing the blade machining experiment, taking into account the experience of designing the blade cross-section and setting the distance between the test cross-sections, 23 cross-sections were equidistantly cut from the blade along the height direction, with cross-section heights ranging from 260mm to 326mm and a spacing of 3mm between adjacent cross-sections. A coordinate measuring machine was used to inspect the entire blade disk, and the projected measured points were spatially registered with the theoretical cross-section lines to obtain the profile error, positional error, and torsion angle error of each cross-section.

[0047] The WT-AP-SG method was used to decompose the profile error of 23 sections of 40 blades obtained in the experiment, and finally the systematic profile error of 23 sections of 40 blades after removing random errors was obtained.

[0048] The system profile error of each blade on each cross section is converted into three-dimensional point coordinates, and a closed curve is fitted using non-uniform rational B-splines (NURBS). The fitted closed curves are grouped according to the cross section height so that the closed curves in the same group correspond to the same theoretical cross section line.

[0049] The theoretical contour lines of each section are discretized using the equal chord height sampling method, where the chord height control parameter h is set to 0.001 mm, and the maximum distance control parameter L... maxThe setting is 0.2mm. The number of theoretical points obtained after discretizing the theoretical profiles of the 23 sections is shown in Table 3. Normal line segments are drawn through each discrete point, intersecting with each closed curve to obtain intersection points. The distance between the intersection point and the corresponding discrete point is the profile error compensation value for each blade at that location, and these are derived sequentially. Based on the Kalman filter algorithm, the sequence data is recursively estimated to calculate the final profile error compensation value for the thin-walled blade at that discrete point, as shown in Table 4.

[0050] Table 3 Number of Discrete Points for 23 Theoretical Cross-Sections Table 4. Final profile error compensation values ​​(mm) at discrete points on each of the 23 cross sections. The Kalman filter algorithm was used to process the positional errors of the 23 cross-sections in the X direction, thus obtaining the system positional errors of the 23 cross-sections in the X direction. The Kalman filter algorithm was also used to process the positional errors of the 23 cross-sections in the Y direction, thus obtaining the system positional errors of the 23 cross-sections in the Y direction. The Kalman filter algorithm was also used to process the torsional angle errors of the 23 cross-sections, thus obtaining the system torsional angle errors of the 23 cross-sections. The system positional errors and system torsional angle errors of the 23 cross-sections are shown in Table 5.

[0051] Table 5. System position error and system torsional angle error at 23 cross sections. Based on the discrete points of 23 theoretical cross-section lines, the system profile error of 23 cross-sections, the system position error of 23 cross-sections, and the system torsional angle error of 23 cross-sections, a machining error compensation model for thin-walled blades was reconstructed. To verify the effectiveness of the machining error compensation model for thin-walled blades, machining experiments of integral bladed disks were conducted based on the compensation model to evaluate its effect on improving blade machining accuracy.

[0052] The equipment and tools used in the experiment are as follows: (1) Machine tool: Kede KMC800SU five-axis vertical machining center; (2) Cutting tools: FR10 end mill, BR4_D16_4° taper ball end mill; (3) Workpiece material: TC17 titanium alloy; (4) Blank dimensions: 260mm (145mm (54mm); (5) Coordinate measuring machine: Leitz Reference Xi 15.9.7; During the experiment, only the theoretical model was replaced with a systematic error compensation model; all other process parameters (such as cutting parameters) remained consistent with those in Tables 2 and 3. Under the same equipment and operating conditions, the entire manufacturing process of the integral bladed disk, from blank to finish machining, was executed, and the resulting compensated model was used to produce the finished part. According to the testing requirements, a coordinate measuring machine was used to measure the blades of the experimental part.

[0053] To analyze the practical effect of the proposed compensation method, the machining accuracy of the blades before and after compensation was compared and verified. To avoid data redundancy, the number of statistical sections was reduced from the original 23 to 11 representative key sections. Based on the machining experimental data before and after compensation, the maximum profile error, positional error, and torsion angle error of the 11 key sections were statistically analyzed and summarized in Table 6. All data were taken as absolute values. The experimental results show that the profile error, positional error, and torsion angle error of the thin-walled blades were significantly reduced after compensation. Specifically, the maximum profile error decreased from 0.044 mm to 0.026 mm, the maximum positional error decreased from 0.043 mm to 0.031 mm, and the maximum torsion angle error decreased from 0.042° to 0.024°. This indicates that the reconstructed compensation model effectively reduced machining errors.

[0054] Table 6 Comparison of machining errors of thin-walled blades before and after compensation The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for error compensation in blade machining systems based on error decomposition and Kalman filtering, characterized in that, include: Step 1: Obtain the measuring points of each section of the processed blade, and project each measuring point onto the corresponding measuring section. Calculate the profile error of each section based on the theoretical section line and the corresponding projection point. Step 2: Sort the profile error of each blade detection section and construct the profile error signal. Use a hybrid algorithm of wavelet threshold denoising combined with amplitude protection SG filtering to process the signal and separate the system profile error after removing random errors. Step 3: Convert the system profile error into three-dimensional coordinates and fit it into a closed curve, grouping them according to the cross-sectional height; obtain discrete points on the theoretical cross-sectional line using the isochord height sampling method with distance constraints; find the intersection point of the line segment from the discrete points, and use the distance between the theoretical point and the intersection point as the compensation value for the blade cross-sectional profile error; Step 4: For the profile error compensation value at the same discrete point, input the error observation value at that position in sequence according to the time order of blade processing, and perform recursive optimal estimation on the sequence data based on the Kalman filter algorithm to obtain the final profile error compensation value of the thin-walled blade at that discrete point. Step 5: Offset each discrete point along the opposite direction of the actual deformation of the blade profile to obtain the corresponding final profile error compensation value to obtain the profile error compensation point coordinates. Perform torsion and offset compensation on the profile error compensation point coordinates to obtain the final compensation point cloud coordinates, and then obtain the compensation curve of each section.

2. The error compensation method for blade machining system based on error decomposition and Kalman filtering according to claim 1, characterized in that, The method for torsional and offset compensation in step 5 is as follows: The positional error and torsional angle error of each section are calculated based on the theoretical section line and the corresponding projection point. The system positional error and system torsional angle error are obtained based on Kalman filtering. Then, the coordinates of each profile error compensation point are twisted and offset in the opposite direction of the actual deformation of the blade profile along the normal vector to obtain the corresponding system positional error and system torsional angle error, thus obtaining the final compensation point cloud coordinates.

3. The error compensation method for blade machining system based on error decomposition and Kalman filtering according to claim 1, characterized in that, Step 2 is as follows: For each detection section of the blade, the contour error is sequentially numbered along the contour detection path of each section; The orderly arranged contour error data is converted into contour error signals for each section. A hybrid filtering algorithm combining wavelet threshold denoising and Savitzky-Golay filtering with amplitude protection is adopted to decompose the contour error signal of each section to obtain the system contour error of each section after removing random errors.

4. The error compensation method for blade machining system based on error decomposition and Kalman filtering according to claim 1, characterized in that, Step 3 specifically involves: The system contour error is converted into three-dimensional point coordinates and fitted into a closed curve. The closed curves are grouped according to the cross-sectional height, so that the closed curves in the same group correspond to the same theoretical cross-sectional line; The equal chord height sampling method with distance constraints is used to discretize each theoretical cross-section line to generate multiple discrete points with equal chord height constraints; By constructing normal line segments at each discrete point, and intersecting them with the closed curves of each blade in the group, the intersection point is obtained. The Euclidean distance between the intersection point and the corresponding discrete point is the profile error compensation value of a single blade at that cross-sectional position.

5. The error compensation method for blade machining system based on error decomposition and Kalman filtering according to claim 4, characterized in that, The distance-constrained isochordal height sampling method introduces a maximum distance control parameter L. max This refers to the maximum allowable distance between two discrete points; the specific steps are as follows: Step a: Set P0 as the starting point and set it as the current point P. p ; Step b: Perform an iterative search using the equal chord height method to determine the next potential measurement point P. n Make the current point P p With P n The chord height is h; Step c: Calculate P p With prediction point P n The distance d between them; if d > L max Then we reject the prediction of point P. n Instead, follow the curved path with a fixed step size L. max Determine the next measurement point P new If d≤L max Then accept the prediction point P. n For the next measurement point P new ; Step d: Update the current point to P new Repeat steps b through c until the process ends; Step e: Export the obtained data points, which are the discrete points.

6. The error compensation method for blade machining system based on error decomposition and Kalman filtering according to claim 3, characterized in that, Step 2, which uses a hybrid algorithm combining wavelet thresholding denoising and amplitude-protected SG filtering to process the signal, specifically involves the following steps: First, the wavelet threshold denoising algorithm is used to perform preliminary denoising on the contour error signals of each section, removing most of the high-frequency noise. Secondly, coarse region detection is performed on the wavelet denoising results to delineate coarse regions that require special processing. Then, SG filtering with amplitude protection is applied to the rough region, and standard SG filtering is applied to the smooth region; Finally, the processing results of the two types of regions are merged and lightly smoothed.

7. The error compensation method for blade machining system based on error decomposition and Kalman filtering according to claim 6, characterized in that, The rough region is the region where the roughness index is greater than the threshold. The threshold for: ; Where, μ r σ is the mean of the roughness exponent; r α is the standard deviation of the roughness index; when R>0.05, α is 0.8, and when R≤0.05, α is 1.5; R is the dynamic range of the signal. The roughness index r i The calculation formula is: ； Where, σ i g is the local standard deviation of the signal dispersion within the window. i The gradient magnitude reflects the local rate of change of the signal; c i To reflect the curvature of the second rate of change of the signal, p i Peak detection is used to identify sudden spikes in a signal.

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